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A finite difference technique for simulating unsteady viscoelastic free surface flows

McKee, S. and Castelo, A. and Cuminato, J.A. and Tomé, M.F. and Mangiavacchi, N. (2002) A finite difference technique for simulating unsteady viscoelastic free surface flows. Journal of Non-Newtonian Fluid Mechanics, 106 (2-3). pp. 61-106. ISSN 0377-0257

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Abstract

This work is concerned with the development of a numerical method capable of simulating viscoelastic free surface flow of an Oldroyd-B fluid. The basic equations governing the flow of an Oldroyd-B fluid are considered. A novel formulation is developed for the computation of the non-Newtonian extra-stress components on rigid boundaries. The full free surface stress conditions are employed. The resulting governing equations are solved by a finite difference method on a staggered grid, influenced by the ideas of the marker-and-cell (MAC) method. Numerical results demonstrating the capabilities of this new technique are presented for a number of problems involving unsteady free surface flows.